The present invention relates to a device and method for sending information and a device and method for receiving information.
Eight-state amplitude modulation (known as xe2x80x9c8-AMxe2x80x9d) can be described as follows. At the input to the communication channel, an alphabet
A={xe2x88x927, xe2x88x925, xe2x88x923, xe2x88x921, 1, 3, 5, 7}
containing eight numbers, referred to as elementary signals, is available. At each instant, r. T, with r=0, 1, 2, . . . , a multiple of an elementary period T, an information source selects a number a of the alphabet A and transmits this number a to a modulator. This modulator produces, between instants r.T and (r+1). T, the electrical signal a.cos(2.xcfx80.f.t) (or more precisely an amplitude signal proportional to a.cos(2.xcfx80.f.t)), where t is the time and f the frequency of the carrier.
To perform this modulation, the modulator uses an energy E(a) substantially proportional to a2.T: E(a)=xcexa2.T., where xcex is the proportionality factor. When the alphabet is as described above, this energy will be measured by one of the numbers xcex. T, 9.xcex. T, 25.xcex. T and 49.xcex. T. The ratio between the greatest and least of these energies is 49. This number is fairly high and it would generally be preferable to reduce it. These considerations constitute the first aspect of the problem.
A second aspect of the problem will now be considered. A signal received is often corrupted, for example by noise. This means that the received signal s(t) corresponding to a transmitted signal a.cos(2.xcfx80.f.t) (a being in the alphabet A) will be measured and evaluated as corresponding to the transmission of b.cos 2.xcfx80.f.t), a formula in which b can be different from a and is moreover not necessarily an element of A.
Sometimes, the noise level or the corruption, during a period T, are sufficiently high to make b.cos(2.xcfx80.f.t) closer to a*.cos(2.xcfx80.f.t) with a* in A, and a* different from a, than to any other transmittable signal, including a.cos (2.xcfx80.f.t). In this case, the decision rule is to estimate that a* has been transmitted and an estimation error appears. It can be demonstrated that, with white Gaussian additive noise conditions, the probability of such an estimation error depends highly on the quantity (a-a*)2.T, and that, the lower the said quantity, the higher will be this probability.
In particular, the probability of estimating a*=xe2x88x927 when a=7 has been transmitted is very low and the probability of estimating a*=3 when a=1 has been transmitted is higher.
In this situation, there is an interest in making the error probabilities uniform: it is not a problem that very low error probabilities increase if at the same time the highest probabilities of error are considerably reduced.
From a third point of view, it will be noted that with the modulation method described above the value of a transmitted elementary signal a remains identical during a period of T seconds. Consequently, the frequency spectrum where the usable energy is transmitted is fairly narrow, which presents different disadvantages in the case of multiple transmission paths or noise dependent on the frequency. In this situation, in fact, there is interest in spreading the available energy in a frequency spectrum of greater width. in addition, in various situations, spectrum spreading is make obligatory by special regulations.
A fourth reason concerns any fading of the signal. When the quantity of energy used during an elementary period of duration T is a quantity E, not dependent on the transmitted information, it is possible to measure the corresponding received energy. In this case, if during an interval of time [r. T, (r+1).T], the received signal s(t) has an energy xcex1.E, it is possible first of all to replace s(t) by s*(t)=s(t)/{square root over (xcex1)} and estimate the transmitted information by processing s*(t).
As a fifth reason, it is wished to have easy access to the information in receiving the noisy message. This property is referred to as an easy decoding method.
Finally, amongst the spectrum spreading properties, the following are also of interest for practical applications:
on the one hand, the error correction properties offered by the set of sequences: these properties are measured by the minimum distance (the Euclidean distance, for example) between two different sequences and it would be wished for this distance to be as great as possible (sixth reason),
on the other hand, the flow of information produced by the spreading system, a flow which it would be wished to be as high as possible for a fixed correction capacity (seventh reason).
It appears that there is a close link between the minimum distance and orthogonality: if two equal energy sequences E are orthogonal, the Euclidean distance d between them is proportional to {square root over (2.E)}. Conjointly, requiring all the sequences of length n and of energy equal to E to be orthogonal in pairs prevents the transmission of more than (log2(n))/T bits of information per second.
A description will now be given of the state of the art concerning these problems and the improvements to be made thereto will also be discussed.
A first way of responding to the third reason mentioned above is to select a sequence h=(h1, . . . , hn) of length n on an alphabet {xe2x88x921, +1} and to replace the transmission of each a by A during the period T by the transmission of n letters a.hi, each during a period T/n. For example, n=8 and h=(+++xe2x88x92+xe2x88x92xe2x88x92xe2x88x92), representing by the sign xe2x80x9c+xe2x80x9d the numerical value xe2x80x9c+1 xe2x80x9d and by the sign xe2x80x9cxe2x88x92xe2x80x9d, the numerical value xe2x80x9cxe2x88x921 xe2x80x9d, a=xe2x88x923 is represented by the sequence (xe2x88x923, xe2x88x923, xe2x88x923, +3, xe2x88x923, +3, +3, +3) in which each component is transmitted for a period T/8. If r =(r1, . . . , r8), is the sequence received, after the transmission of a certain a.h, an estimation of a is the element xc3xa2 of A whose value is as close as possible to the mean of the ri.hi values, i ranging from 1 to 8.
Therefore, in addition to the third reason, this method is good for the fifth reason mentioned above. However, it satisfies neither the first nor the fourth, nor the sixth, nor the seventh reasons mentioned above and it has only few qualities with regard to the second reason.
A second solution (see the document EP-A-94.400.936.4, K. Saito et al.) consists of choosing a square Hadamard matrix H of size nxc3x97n, that is to say a matrix on the alphabet {xe2x88x921, +1} which satisfies H.HT=n.In, with HT being the transposed matrix of H and In being the identity matrix of size nxc3x97n. Let also H* be any sub-matrix 7xc3x97n of H and let the information be represented by a sequence of 7-tuples on {xe2x88x921, +1}. Also let a be such a 7-tuple and let v=(v1, . . . vn) be the n-tuple on A given by v=a. H*.
Each component vi, of v is transmitted for a period T/n. For example, with n=12, a=[+xe2x88x92+xe2x88x92+++]and       H    *    =                    +                    -                    -                    +                    +                    +                    -                    -                    +                    +                    -                    +                            -                    -                    +                    +                    +                    +                    -                    +                    -                    -                    +                    +                            -                    +                    -                    +                    +                    +                    +                    -                    -                    +                    +                    -                            +                    +                    -                    +                    +                    -                    +                    +                    +                    -                    +                    +                            +                    -                    +                    +                    -                    +                    +                    +                    +                    +                    +                    -                            -                    +                    +                    -                    +                    +                    +                    +                    +                    +                    -                    +                            +                    -                    +                    -                    +                    -                    +                    -                    -                    +                    +                    +            
v is equal to (1, xe2x88x921, 1, xe2x88x921, 1, 3, 3, xe2x88x923, 1, 7, xe2x88x921, xe2x88x921). This method is effective vis-a-vis the first five reasons mentioned above. In particular, with regard to the first reason, the above method makes uniform the energy used over all the twelve intervals of time of duration T/12. However, this method does not lead to a good balance between the last two reasons.
The present invention sets out to remedy these drawbacks.
In the remainder of the description:
The expression xe2x80x9cmatrix with an orthogonal dominantxe2x80x9d designates a square matrix H of real numbers such that the absolute value of the diagonal elements of the matrix H.HT resulting from the matrix product of the matrix H and the transposed matrix HT of the matrix H, is at least an order of magnitude greater than the absolute value of the other elements of this matrix H.HT,
the expression xe2x80x9corthogonal matrixxe2x80x9d designates a square matrix H of real numbers such that the diagonal elements of the matrix H.HT are non-null and the other elements of the matrix H.HT are null.
To this end, according to a first aspect, the present invention relates to a method of transmitting information on a transmission channel associated with a first numerical alphabet, each number in the said first alphabet being proportional to a physical quantity which can be transmitted on the said channel, characterised in that it takes into account:
a matrix with an orthogonal dominant H of dimensions nxc3x97n on a second numerical alphabet including at least three different non-null values, and
a set of at least one sub-matrix of the said matrix H, each sub-matrix of the said set containing a number p greater than or equal to 2 of rows of the matrix H, and in that it includes
an operation of conjoint selection of:
one of the sub-matrixes of the said set, and
a p-tuple of real numbers referred to as the xe2x80x9crow of coefficientsxe2x80x9d,
in such a way that the matrix product of the said row and the said selected sub-matrix supplies a sequence of numbers of the said first alphabet, the said selected sub-matrix and the said row of coefficients conjointly representing the information to be transmitted; and
an operation of representing the information to be transmitted by a said sequence.
By virtue of these provisions, when the transmission channel causes no corruption of the symbols of the first alphabet, by producing, at the output of the said transmission channel, the scalar product of the received sequence, and each of the rows of the matrix H, there is obtained:
a practically null value for each of the n-p rows which do not form part of the selected sub-matrix, and
for each of the p rows forming part of the said selected sub-matrix, a value which is practically proportional to the element of the row of coefficients which corresponded to it during the conjoint selection operation, for the purpose of the matrix product.
In this way all the information is recovered on receipt of the sequence representing the transmitted information.
When the transmission channel causes corruption of the symbols of the first alphabet, by producing, at the output of the said transmission channel, the scalar product of the received sequence, and each of the rows of the matrix H, n numbers are obtained. Amongst these, on the one hand n-p numbers are obtained from the rows of the matrix H external to the sub-matrix selected on sending, and they are practically null in the absence of corruption, and, on the other hand, p numbers are obtained from the rows of the sub-matrix selected on sending and, in the absence of corruption, they are respectively practically equal to a multiple of the p numbers appearing in the row of coefficients.
When the corruption is not too great, by processing the values of the scalar products mentioned above, it is possible to recover all the transmitted information.
The advantages associated with the disclosure of the invention include:
during an elementary period of duration T, the value of the signal transmitted on the channel can vary n times, whilst the sum of the squares of these n values will be constant,
the variability of the output level allows more flexibility and, all other things being equal, improves the minimum distance between signal sequences,
the spectrum width is essentially multiplied by n,
the matrix H being orthogonal, access to the information is easy during decoding,
the minimum distance being improved, the error corruption capacity is also,
for a fixed error correction capacity, the information transmission rate is improved.
These advantages correspond respectively to reasons 1, 2, 3, 5, 6 and 7 mentioned above. In particular the invention is efficacious with regard to the balance of the criteria mentioned in the last two reasons.
According to first preferential characteristics, the orthogonal dominant matrix H taken into account by the transmission method as briefly disclosed above, is an orthogonal matrix, and, during the conjoint selection operation, a sub-matrix of the said orthogonal matrix H is selected.
By virtue of these provisions, when the transmission channel causes a corruption of the symbols of the first alphabet, by effecting, at the output of the said transmission channel, the scalar product of the sequence received, and each of the rows of the matrix H, n numbers are obtained. Amongst these, on the one hand n-p numbers are obtained from the rows of the matrix H external to the sub-matrix selected on sending, and they are precisely null in the absence of corruption, and, on the other hand, p numbers are obtained from the rows of the sub-matrix selected on sending and, in the absence of corruption, they are respectively precisely equal to a multiple of the p numbers appearing in the row of coefficients.
Processing of the received sequence is therefore simplified.
According to second preferential characteristics, during the conjoint selection operation, a sub-matrix of a matrix H is selected for which the diagonal elements of the matrix H.HT resulting from the matrix product of the matrix H by the transposed matrix HT of the matrix H, are all equal to the same value M. The matrix H is then termed xe2x80x9cbalancedxe2x80x9d.
By virtue of these provisions, when the transmission channel causes a corruption of the symbols of the first alphabet, by effecting, at the output of the said transmission channel, the scalar product of the sequence received, and each of the rows of the matrix H, n numbers are obtained. Amongst these, on the one hand n-p numbers are obtained from the rows of the matrix H external to the sub-matrix selected on sending, and they are precisely null in the absence of corruption, and, on the other hand, p numbers are obtained from the rows of the sub-matrix selected on sending and, in the absence of corruption, they are respectively practically equal to M times the p numbers appearing in the row of coefficients.
According to third preferential characteristics, during the conjoint selection operation, the coefficients in the row of coefficients all have the same absolute value.
Processing of the received sequence is thus simplified.
According to other preferential characteristics, during the conjoint selection operation:
the sub-matrix of the said set, and
the p-tuple of real numbers referred to as the xe2x80x9crow of coefficientsxe2x80x9d
are selected so that the matrix product of the said row and the said selected sub-matrix supplies a sequence of numbers of the said first alphabet, the sum of whose squares is a predetermined value.
By virtue of these provisions, the energy expended over an elementary period of duration T does not vary between two elementary periods.
According to particular characteristics:
during the conjoint selection operation, at least two sub-matrixes are able to be selected, and
during the representation operation, the choice of the sub-matrix producing the said sequence represents at least part of the information to be transmitted.
By virtue of these provisions, at the output of the transmission channel, by effecting the scalar product of the received sequence and the rows of the orthogonal matrix, a sequence of values is obtained representing the choice of the sub-matrix which was used on sending.
It is then possible, for example, to consider that the rows used are those for which the absolute values of the scalar products with the received sequence are the highest.
According to other preferential characteristics:
during the conjoint selection operation, the row of coefficients can take at least two different values, and
during the representation operation, the choice of the value of the row of coefficients represents at least part of the information to be transmitted.
By virtue of these provisions, at the output of the transmission channel, by effecting the scalar product of the received sequence and the rows of the orthogonal matrix, there is obtained a sequence of values representing elements of the row of coefficients which was selected, as well as values of the p-tuple of numbers forming the row of coefficients.
It is in fact possible, for example, to consider that the rows for the matrix H selected during the conjoint selection operation are those for which the absolute values of their scalar product with the sequence received are the highest and that the numbers in the row of coefficients are approximately proportional (by the number M appearing in the equation H.HT=M.In) to the corresponding elements of the n-tuple obtained by producing the matrix product of the n-tuple received and the matrix HT.
More generally, it is possible to consider that the coefficients used are those which are the most probable as a function of a modelling of the corruption caused by the channel.
According to a second aspect, the invention relates to a method of receiving information by means of a transmission channel associated with a first numerical alphabet, each number in the said first alphabet being proportional to a physical quantity which can be transmitted on the said channel, a method including an operation of receiving sequences of numbers, characterised in that it takes into account:
a matrix with an orthogonal dominant H of dimensions nxc3x97n on a second numerical alphabet including at least three different non-null values, and
a set of at least one sub-matrix of the said matrix H, each sub-matrix of the said set containing a number p greater than or equal to 2 of rows of the matrix H, and in that it includes:
an operation of the conjoint determination of:
one of the sub-matrixes of the said set, and
a p-tuple of real numbers referred to as the xe2x80x9crow of coefficientsxe2x80x9d,
the matrix product of the said row and the said selected sub-matrix corresponding to the said received sequence, the said selected sub-matrix and the said selected row of coefficients conjointly representing the information to be transmitted; and
an operation of conjoint matching of the said sub-matrix and the said row of coefficients with the so-called xe2x80x9ctransmittedxe2x80x9d information.
According to a third aspect, the invention relates to a device for transmitting information on a transmission channel associated with a first numerical alphabet, each number in the said first alphabet being proportional to a physical quantity which can be transmitted on the said channel, characterised in that it has:
a memory adapted to store a set of at least one sub-matrix of a matrix with an orthogonal dominant H of dimensions nxc3x97n on a second numerical alphabet including at least three different non-null values, each sub-matrix of the said set containing a number p greater than or equal to 2 of rows of the matrix H, a means of conjoint selection of:
one of the sub-matrixes of the said set, and
a row of p coefficients equal to +1 or xe2x88x921,
so that the matrix product of the said row and the said selected sub-matrix supplies a sequence of numbers of the said first alphabet, the said selected sub-matrix and the said selected row of coefficients conjointly representing the information to be transmitted; and
a means of representing the information to be transmitted by a said sequence.
According to a fourth aspect, the invention relates to a device for receiving information by means of a transmission channel associated with a first numerical alphabet, each number in the said first alphabet being proportional to a physical quantity which can be transmitted on the said channel, a device including at least one means of receiving sequences of numbers, characterised in that it has:
a memory adapted to store a set of at least one sub-matrix of a matrix with an orthogonal dominant H of dimensions nxc3x97n on a second numerical alphabet including at least three different non-null values, each sub-matrix of the said set containing a number p greater than or equal to 2 of rows of the matrix H, a means of conjoint determination of:
one of the sub-matrixes of the said set, and
a p-tuple of real numbers referred to as the xe2x80x9crow of coefficientsxe2x80x9d,
the matrix product of the said row and the said selected sub-matrix corresponding to the said received sequence, the said selected sub-matrix and the said selected row of coefficients conjointly representing information to be transmitted; and
a means of joint matching of the said sub-matrix and the said row of coefficients with so-called xe2x80x9ctransmittedxe2x80x9d information.
The invention also relates to a camera, a facsimile machine, a photographic apparatus, a computer, characterised in that they have a device as briefly disclosed above.
The invention also relates to:
a means of storing information which can be read by a computer or a microprocessor storing instructions of a computer program, characterised in that it enables the method of the invention as briefly disclosed above to be implemented, and
a means of storing information which can be read by a computer or a microprocessor storing data resulting from the implementation of the method as briefly disclosed above,
a means, partially or totally removable, of storing information which can be read by a computer or microprocessor storing instructions of a computer program, characterised in that it enables the method of the invention as briefly disclosed above to be implemented, and
a means, partially or totally removable, of storing information, which can be read by a computer or a microprocessor storing data resulting from the implementation of the method as briefly disclosed above.
The preferential or special characteristics, and the advantages of the transmission device, of the receiving device and method, of this camera, of this facsimile machine, of this photographic apparatus and of this computer and of these information storage means, being identical to those of the transmission device and method, these advantages are not restated here.